% Code Matlab de génération de graphique C-CAPM
% Illustration de Mehra et Prescott (JME, 1985).
% génération de prime de risque et rendement certain réalisables,
% en fonction de l'aversion au risque (alpha) et facteur d'actualisation (beta)
% auteur: Pascal St-Amour, hiver 2001
% cours 6, 6-203-79, TMC
mu = 0.018;
delta = 0.036;
phi = 0.43;
lambda_1 = 1+mu+delta;
lambda_2 = 1+mu-delta;
phi_11 = phi;		phi_12 = 1-phi;
phi_21 = 1-phi;	phi_22 = phi;
[alpha,beta] = meshgrid(0:0.1:10,0:0.01:1);
a_11 = beta.*phi_11.*lambda_1.^(1-alpha);
a_12 = beta.*phi_12.*lambda_2.^(1-alpha);
a_21 = beta.*phi_21.*lambda_1.^(1-alpha);
a_22 = beta.*phi_22.*lambda_2.^(1-alpha);
q_1 = beta.*(phi_11.*lambda_1.^(-alpha) + phi_12.*lambda_2.^(-alpha));
q_2 = beta.*(phi_21.*lambda_1.^(-alpha) + phi_22.*lambda_2.^(-alpha));
[n,m] = size(alpha);
for i = 1:n
   for j = 1:m
      A = [a_11(i,j) a_12(i,j); a_21(i,j) a_22(i,j)];
      B = [a_11(i,j)+a_12(i,j); a_21(i,j)+a_22(i,j)];
      W = (ones(2,2) - A)\B;
      W_1(i,j) = W(1,1);
      W_2(i,j) = W(2,1);
      Re_1 = phi_11.*(W_1(i,j)+1)./W_1(i,j) *lambda_1 + phi_12.*(W_2(i,j)+1)./W_1(i,j) *lambda_2;
      Re_2 = phi_21.*(W_1(i,j)+1)./W_2(i,j) *lambda_1 + phi_22.*(W_2(i,j)+1)./W_2(i,j) *lambda_2;
      Re(i,j) = 0.5.*Re_1 + 0.5*Re_2;
      Rf(i,j) = 0.5.*1./q_1(i,j) + 0.5.*1./q_2(i,j);
   end
end
figure(1)
mesh(alpha,beta,Rf)
xlabel('alpha'); ylabel('beta'); zlabel('Rf')
figure(2)
mesh(alpha,beta,Re-Rf)
xlabel('alpha'); ylabel('beta'); zlabel('Re-Rf')